Local Structural Features Threaten Privacy across Social Networks

Can only a handful of structural features and no knowledge of link-level connectivity threaten privacy of individuals in a social network? Specifically, can we use a small number of local structural features defined on nodes (such as degree, clustering coefficient, average degree of neighbors, average clustering coefficient of neighbors, etc) to reduce the uncertainty of individuals’ identities? Our work shows that the answer is yes. We detail how without direct access to the adjacency matrix, we can use the information in an auxiliary graph to effectively and efficiently reduce the uncertainty of any individual’s identity. To our knowledge, our work is the first of its kind that uses only structural features in order to reduce the uncertainty of an individual’s identity to the best possible set of candidates. In addition to being efficient (i.e., sub-quadratic computation), our approach automatically selects the appropriate size of the best possible set of candidates. Previous works assume the adjacency matrix of the anonymized graph is released; and hence rely on the sparsity of the human behavior exhibited in the adjacency matrix. The node × feature matrix is not sparse, making the re-identification problem a lot harder. Our experiments involve multiple synthetic and real graphs plus different noise models and parameter settings. On average for 84.5% of the individuals in real graphs, we are able to reduce the uncertainty by 85.4%. In synthetic graphs, on average for 82% of the nodes, we are able to reduce the uncertainty by 60%. We compare our approach to three baseline methods; and explain our results in terms of Jaccard Similarity and the number of Lookalikes between the original and auxiliary graphs.